If they just met recently, I'm not sure why she would be the one to call you and tell you she would like you all to go to lunch together. But in any case I agree with Tone, you don't even know this girl and your wanting to call her to go out...for what? to get back at your ex? That's putting this girl in a very ackward situation and setting yoruself up for a downfall because I don't see her dropping your ex as a friend for someone she doesn't knows..so your Ex would be around a lot.
Don't worry about your Ex knowing your over her or whatever. You ahve to think of yourself not her, you have to move on and get yourself away from her or else your just going to make yourself miserable.
If you can't handle the thorns, don't crave the rose!!